## Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra

Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S.**Journal of Physics A. Mathematical and General**38, no. 1 (2005), 153 — 174

## Abstract

We argue that one can factorize the difference equation of hypergeometric type on the non-uniform lattices in general case. It is shown that in the most cases of *q*-linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra su*q*(1,1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the *q*-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.

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## BibTeX

@article {MR2126099, AUTHOR={\'{A}lvarez-Nodarse, R. and Atakishiyev, N. M. and Costas-Santos, R. S.}, TITLE={Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra}, JOURNAL={J. Phys. A}, FJOURNAL={Journal of Physics A. Mathematical and General}, VOLUME={38}, YEAR={2005}, NUMBER={1}, PAGES={153--174}, ISSN={0305-4470}, MRCLASS={39A13 (33D15)}, ZBL={1079.33017}, MRNUMBER={2126099}, MRREVIEWER={Lucia Di Vizio}, DOI={10.1088/0305-4470/38/1/011}, URL={https://doi.org/10.1088/0305-4470/38/1/011}, }